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Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?

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This problem is about investigating whether it is possible to start at one vertex of a platonic solid and visit every other vertex once only returning to the vertex you started at.

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Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

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The aim of the game is to slide the green square from the top right hand corner to the bottom left hand corner in the least number of moves.

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Do you know how to find the area of a triangle? You can count the squares. What happens if we turn the triangle on end? Press the button and see. Try counting the number of units in the triangle now. . . .

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Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?

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It's easy to work out the areas of most squares that we meet, but what if they were tilted?

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Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?

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When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...

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Try entering different sets of numbers in the number pyramids. How does the total at the top change?

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Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?

This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.

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We can show that (x + 1)² = x² + 2x + 1 by considering the area of an (x + 1) by (x + 1) square. Show in a similar way that (x + 2)² = x² + 4x + 4

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A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

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Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.

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A game for 2 players that can be played online. Players take it in turns to select a word from the 9 words given. The aim is to select all the occurrences of the same letter.

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A tilted square is a square with no horizontal sides. Can you devise a general instruction for the construction of a square when you are given just one of its sides?

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Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

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A circle rolls around the outside edge of a square so that its circumference always touches the edge of the square. Can you describe the locus of the centre of the circle?

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A and B are two interlocking cogwheels having p teeth and q teeth respectively. One tooth on B is painted red. Find the values of p and q for which the red tooth on B contacts every gap on the. . . .

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In this game you are challenged to gain more columns of lily pads than your opponent.

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What is the greatest number of squares you can make by overlapping three squares?

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Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis?

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Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

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Use an Excel to investigate division. Explore the relationships between the process elements using an interactive spreadsheet.

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What can you say about the values of n that make $7^n + 3^n$ a multiple of 10? Are there other pairs of integers between 1 and 10 which have similar properties?

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Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?

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Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

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A game for two people that can be played with pencils and paper. Combine your knowledge of coordinates with some strategic thinking.

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A game in which players take it in turns to choose a number. Can you block your opponent?

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Seeing Squares game for an adult and child. Can you come up with a way of always winning this game?

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Train game for an adult and child. Who will be the first to make the train?

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In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?

The 2012 primary advent calendar features twenty-four of our posters, one for each day in the run-up to Christmas.

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A red square and a blue square overlap so that the corner of the red square rests on the centre of the blue square. Show that, whatever the orientation of the red square, it covers a quarter of the. . . .

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Ahmed has some wooden planks to use for three sides of a rabbit run against the shed. What quadrilaterals would he be able to make with the planks of different lengths?

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Can you explain the strategy for winning this game with any target?

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Can you work out what step size to take to ensure you visit all the dots on the circle?

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Two circles of equal radius touch at P. One circle is fixed whilst the other moves, rolling without slipping, all the way round. How many times does the moving coin revolve before returning to P?

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The computer has made a rectangle and will tell you the number of spots it uses in total. Can you find out where the rectangle is?

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This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

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Here is a chance to play a fractions version of the classic Countdown Game.

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Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

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A train building game for two players. Can you be the one to complete the train?

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Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?

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Calculate the fractional amounts of money to match pairs of cards with the same value.